For a molecule that does not dissociate in water, such as R = 0.082 atm L/mol K glucose or urea, a solution containing 1 mmol/L of these T = 310 °K •Fig. 1.8 Schematicrepresentationofosmoticwatermovementandthegenerationofanosmoticpressure.CompartmentAandcompartmentBareseparatedbyasemipermeablemembrane(i.e.,themembraneishighlypermeablebywaterbutimpermeablebysolute).CompartmentAcontainsasolute,whereascompartmentBcontainsonlydistilledwater.Overtime,watermovesbyosmosisfromcompartmentBtocompartmentA.(Note:Thiswatermovementisdrivenbytheconcentrationgradientforwater.BecauseofthepresenceofsoluteparticlesincompartmentA,theconcentrationofwaterincompartmentAislessthanthatincompartmentB.Consequently,watermovesacrossthesemipermeablemembranefromcompartmentBtocompartmentAdownitsconcentrationgradient.)ThiscausestheleveloffluidtoberaisedincompartmentAandloweredincompartmentB.Atequilibrium,thehydrostaticpressureexertedbythecolumnofwater(h)stopsthenetmovementofwaterfromcompartmentBtoA.Thusatequilibrium,thehydrostaticpressureisequalandoppositetotheosmoticpressureexertedbythesoluteparticlesincompartmentA.(RedrawnfromKoeppenBM,StantonBA.Renal Physiology. 4thed.St.Louis:Mosby;2006.)
Because 1 atm equals 760 mm Hg at sea level, π for this solution can also be expressed as 19.3 mm Hg. Alternatively, osmotic pressure is expressed in terms of osmolarity (see the following section). Regardless of the molecule, a solution containing 1 mmol/L of the molecule therefore exerts an osmotic pressure proportional to 1 mOsm/L.
For molecules that dissociate in a solution, n of eq. 1.7 will have a value other than 1. For example, a 150-mmol/L solution of NaCl has an osmolarity of approximately 300 mOsm/L because each molecule of NaCl dissociates into a Na+ and a Cl− ion (i.e., n = 2).
If dissociation of a molecule into its component ions is not complete, n will not be an integer. Accordingly, osmolarity for any solution can be calculated as follows:
Equation 1.8
Osmolarity = concentration × number of dissociable particles mOsm/L = mmol/L × number of particles
The terms osmolarity and osmolality are frequently confused and incorrectly interchanged. Osmolarity refers to the osmotic pressure generated by the dissolved solute molecules in 1 L of solvent, whereas osmolality is the number of molecules dissolved in 1 kg of solvent. For a dilute solution, the difference between osmolarity and osmolality is cNaCl does not completely dissociate in water. The value for n is 1.88 rather than 2. However, for simplicity, the value of 2 is most often used.
insignificant. Measurements of osmolarity are temperature dependent because the volume of the solvent varies with temperature (i.e., the volume is larger at higher temperatures). In contrast, osmolality, which is based on the mass of the solvent, is temperature independent. For this reason, osmolality is the preferred term for biologic systems and is used throughout this book. Because the solvent in biological solutions and bodily fluids is water, and because of the dilute nature of biological solutions and bodily solutions, osmolalities are expressed as milliosmoles per kilogram of water (mOsm/kg H2O).